A lead rod and a common glass rod both have the same length when at 20 .0 degrees Celsius. The lead rod is heated to 50.0 degrees Celsius. To what temperature must the glass rod e heated so that they are again at the same length?

To solve this problem, we can use the concept of linear expansion. When an object is heated, its length increases due to thermal expansion.

The formula to calculate the change in length (ΔL) is given by:
ΔL = α * L0 * ΔT

Where:
ΔL is the change in length
α is the coefficient of linear expansion
L0 is the original length of the rod
ΔT is the change in temperature

Given that the lead rod and the glass rod have the same original length and are both heated, we can equate the change in length for both rods:

ΔL_lead = ΔL_glass

α_lead * L0_lead * ΔT_lead = α_glass * L0_glass * ΔT_glass

We are given that the original temperature is 20.0 degrees Celsius. So, ΔT_lead = 50.0 - 20.0 = 30.0 degrees Celsius

Let's assume that the lead rod has a coefficient of linear expansion, α_lead, and the glass rod has a coefficient of linear expansion, α_glass.

We need to find the temperature, ΔT_glass, at which the glass rod must be heated so that both rods have the same length again.

Now rearranging the equation, we get:
ΔT_glass = (α_lead * L0_lead * ΔT_lead) / (α_glass * L0_glass)

Substituting the values we know:
ΔT_glass = (α_lead * L0_lead * 30.0) / (α_glass * L0_glass)

Since we want ΔT_glass, we need to know the ratio of the coefficients of linear expansion, α_lead/α_glass. This value can be found in physics reference books or online sources specific to lead and common glass. Once you have this ratio, substitute it into the equation to find the value of ΔT_glass.

Note: The assumption here is that the coefficient of linear expansion is linear over the given temperature range and that the rods undergo uniform expansion.